Aspects of T-duality in Open Strings

TL;DR

This paper explores T-duality in open strings using canonical transformations, revealing how boundary conditions map and showing that non-abelian duals can be curved D-branes, with extensions to supersymmetric models.

Contribution

It introduces a canonical transformation approach to T-duality in open strings, providing explicit boundary condition mappings and analyzing non-abelian duality effects.

Findings

Duality maps boundary conditions explicitly

Non-abelian duals can be curved D-branes

Extension to supersymmetric sigma models

Abstract

We study T-duality for open strings in various $D$-manifolds in the approach of canonical transformations. We show that this approach is particularly useful to study the mapping of the boundary conditions since it provides an explicit relation between initial and dual variables. We consider non-abelian duality transformations and show that under some restrictions the dual is a curved $(d-{\rm dim}G-1)$ D-brane, where $d$ is the dimension of the space-time and $G$ the non-abelian symmetry group. The generalization to $N=1$ supersymmetric sigma models with abelian and non-abelian isometries is also considered.